Bracing drills like Stuart McGill's "big 3" and stuff like ab wheel and stir the pot are likely to help the most. Personally, I stopped training abs once I learned to brace properly and my lifts have only gone up as a result. Some people might benefit from training abs (especially if you don't know how to brace properly, which McGill's exercises will teach you) but it comes at a cost to recovery as well. I think that to increase the squat and deadlift I'm better off squatting and deadlifting more rather than putting that time and energy into ab work.

Because lots of kids my age, and people who don't really lift like that in general, may claim to be squatting a certain amount of weight, while depth be not even parallel. I'm trying to make sure I sound credible.

You are squatting to depth, we have established that, no need to keep reminding us. I just get annoyed with all the ATG talk, anytime you look at the comments on pretty much any powerlifting video on YouTube there are a bunch of idiots saying "hey man, that's not ATG" or "but he's wearing a belt, that's not raw". I just want to make sure that you don't follow in their footsteps. When I do high bar squats I'm going at least a deep as you but I have never gotten the urge to call it ATG.

Lol yea I'm not like that. I've realized that I'm pretty strong for my age though, and with my numbers perceived depth becomes questionable. For example, the football team posts numbers for each student in my school weight room, and even though they are high, NONE of them squat to parallel.